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Rounding Decimals

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Basics on the topic Rounding Decimals

Rounding Decimals: A Step-by-Step Guide

Welcome to our exciting journey into the world of rounding decimals! Here, we aim to simplify complex numbers, making them more manageable and understandable, by using rounding to different place value.

Rounding Decimals – Definition

Rounding decimals is used in our daily lives very often - it helps when estimating money, measurements or distances - therefore, learning how to round is a valuable skill not only in but also outside of school.

Rounding decimals is about approximating, or estimating, a decimal to a certain place value.

Are you ready to become a rounding expert? Let’s jump in!

Decimals and Rounding

Understanding decimals is key to mastering how to round them. A decimal number represents an equal part of a whole, just like a fraction. If you're new to decimals or need a refresher, our video What is a Decimal? is a perfect starting place.

Rounding decimals is similar to rounding whole numbers. Brush up on this foundational skill by checking out Rounding Multi Digit Numbers.

Feeling confident? Let's proceed to the world of rounding decimals together!

Understanding Rounding Decimals – Rules

When rounding decimals, it is important to follow a few simple rules:

Rule Description
To round to the nearest tenth Check the hundredth place
To round to the nearest hundredth Check the thousandth place
The determining digit is 5 or higher Round up
The determining digit is lower than 5 Round down
What is decimal rounding?
When do we round up?

Rounding Decimals – Examples

Let’s explore some examples. Imagine rounding the number 3.673:

To the nearest tenth: Look at the hundredth place (7). Since 7 > 5, round up to 3.7.

27092_ToV-01.svg

27092_ToV-03.svg

To the nearest hundredth: Look at the thousandth place (3). Since 3 < 5, round down to 3.67.

27092_ToV-02.svg

27092_ToV-04.svg

Rounding Decimals – Guided Practice

Try rounding the number 9.736 to the nearest tenth.

Look at the digit in the hundredth place. What is it?
Decide if this digit rounds the tenths up or down.
Write the rounded decimal.

Try rounding the number 9.736 to the nearest hundredth.

Look at the digit in the thousandth place. What is it?
Decide if this digit rounds the hundredths up or down.
Write the rounded decimal.

Rounding Decimals – Exercises

Now that you are familiar with rounding rules and have seen a couple of examples, let’s try to complete a couple of trickier rounding exercises.

Round 3.78 to the nearest whole number.
Round 6.53 to the nearest tenth.
Round 2.849 to the nearest hundredth.
Round 0.57 to the nearest whole number.
Round 4.9400 to the nearest tenth.
Challenge exercise! List all decimals (to two decimal places) that will round to 3.4 when rounded to the nearest tenth.

Rounding Decimals – Summary

  • A decimal number represents an equal part of a whole, just like a fraction.

  • Rounding decimals is about approximating, or estimating, a decimal to a certain place value.

  • Rounding decimals is used in our daily lives very often - it helps when estimating money, measurements or distances.

  • Rounding to the nearest tenth: Look at the hundredth place. Round up if ≥ 5, otherwise round down.

  • Rounding to the nearest hundredth: Look at the thousandth place. Round up if ≥ 5, otherwise round down.

Frequently Asked Questions – Rounding decimals

What is rounding decimals?
Why do we round decimals?
What are the basic steps in rounding decimals?
How do you round to the nearest tenth?
How do you round to the nearest hundredth?
Can you round a decimal to a whole number?
What happens to the digits after the rounding point?
Does rounding a decimal always increase the number?
Is rounding decimals important in real life?

Transcript Rounding Decimals

The day of the long-awaited concert is finally here for Luis and Kai! They have all the details of the journey planned out, but they want to estimate how far they're travelling so they are prepared. We can do this by rounding decimals. Rounding decimals is a process that is used to approximate a number to a specific place value. This is useful in maths and when working with money, measurements and distances to help you get a good estimate. Rounding decimals follows similar steps and rules to rounding whole numbers. First, identify the place value that you are rounding to. If we were rounding to the tenth place, we would start here. Then, look at the digit to the right. If the value of the digit to the right is less than five, keep the number the same. If the value of the digit to the right is five or more, round the number up to the next one. When you write the rounded decimal number, get rid of every digit to the right of the number you are rounding. You only do this when rounding in the decimal places. Luis and Kai are ready for our help now! Their first stop is the train station, which is seven point two three four five miles away. Round this number to the hundredth place. Here, we identify the digit in the hundredth place, a three. Now look to the right of this value, which is a four. Since four is less than five, we round down, which means the three stays as it is. When we write the rounded decimal, we lose the four and five after the hundredth place, since we rounded to the hundredth place. Seven point two three four five rounded to the hundredth place is seven point two three! The train station is seven point two three, or seven and twenty three hundredths, miles away. From the train station, the concert is thirty-five point eight nine three miles away. Let's see if we can round this number to the nearest tenths place. Pause the video to solve the problem, and press play when you are ready for the solution. Identify the tenth place value, which is eight. Look at the value to the right, which is a nine. Nine is greater than five, so we round up. Thirty-five point eight nine three to the nearest tenth place is thirty-five point nine, or thirty five and nine tenths. The concert is thirty-five point nine, or thirty five and nine-tenths, miles away. Before we check out the concert, let's wrap it up! To summarise, rounding decimals is a similar process to rounding whole numbers. Simply identify the place value you're rounding and look at the digit to the right. If it's less than five, round down and if it's five or above, round up and then drop every digit after the place value you're rounding to. Let's see if Kai and Luis made it to the concert! Looks like a rocking concert!

Rounding Decimals exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Rounding Decimals.
  • Approximately how far is it to the concert?

    Hints

    To round to the nearest tenth, look at the digit in the tenths place and then at the digit to the right.

    If it is 4 or below, keep the value in the tenths place the same. If it is 5 or above, round up.

    To round to the nearest hundredth, look at the digit in the hundredths place and then at the digit to the right.

    If it is 4 or below, keep the value in the hundredths place the same. If it is 5 or above, round up.

    Solution

    17.9374

    Rounded to the nearest tenth: 17.9 miles

    • Look at the digit in the tenths place, 9, then look at the digit to the right, 3, so we keep the value in the tenths place the same.
    Rounded to the nearest hundredth: 17.94 miles

    • Look at the digit in the hundredths place, 3, then look at the digit to the right, 7, so we round up.
  • Can you round these numbers to the nearest tenth?

    Hints

    Look at the number in the tenths place and then at the digit to the right.

    If the digit to the right is 4 or below, keep the value in the tenths place the same.

    If the digit to the right is 5 or above, round up.

    For example, if we were round 3.583 to the nearest tenth, we would look at the digit in the tenths place which is 5.

    We would then look at the digit to the right which is 8. This means we would round up.

    3.583 rounded to the nearest tenth is 3.6.

    Solution

    Here we can see the matching pairs.

    • 21.234 rounded to the nearest tenth is 21.2
    • 28.875 rounded to the nearest tenth is 28.9
    • 21.438 rounded to the nearest tenth is 21.4
    • 28.1023 rounded to the nearest tenth is 28.1
  • Can you round these decimals?

    Hints

    Remember, if the digit to the right of the digit you are rounding to is 4 or below, the digit you are rounding to stays the same.

    If it is 5 or above, round up.

    If you are rounding to the nearest tenth, there should be one digit to the right of the decimal point.

    If you are rounding to the nearest hundredth, there should be two digits to the right of the decimal point.

    Let's work through an example:

    Round 1.3156 to the nearest hundredth.

    We would round up because the digit to the right of the hundredth place is 5 or above.

    The correct answer would be 1.32.

    Solution

    1) Round 8.7493 to the nearest hundredth.

    Correct answer: 8.75

    2) Round 4.5932 to the nearest tenth.

    Correct answer: 4.6

    3) Round 17.6434 to the nearest hundredth.

    Correct answer: 17.64

  • Round these decimals to the nearest hundredth.

    Hints

    When rounding to the nearest hundredth, look at the digit in the hundredths place and then at the digit to the right.

    If the digit to the right is 4 or below, round down.

    If the digit to the right is 5 or above, round up.

    For example, in 12.6653, there is a 6 in the hundredths place and the number to the right is 5. This means we round up.

    Solution

    Numbers that round to 12.34

    • 12.3376
    • 12.3445
    • 12.3412
    Numbers that round to 12.45

    • 12.4521
    • 12.4487
    Numbers that round to 12.67

    • 12.6653
    • 12.6743
    All of these numbers are rounded to the nearest hundredth.

  • To the nearest tenth, how far away is the party?

    Hints

    When rounding to the nearest tenth, look at the digit in the tenths place and then at the digit to the right.

    If the digit to the right is 4 or below, keep the value in the tenths place the same.

    If the digit to the right is 5 or above round up.

    Here, the digit to the right is 8, so we need to round up.

    The correct answer has one digit to the right of the decimal point.

    Solution

    The correct answer is 2.5 kilometres.

    When rounding 2.4832 to the nearest tenth, we look at the digit in the tenths place, 4, and then at the digit to the right, 8.

    As 8 is 5 or above, we round up.

  • The journey to the theme park.

    Hints

    When rounding to the nearest tenth, look at the digit in the tenths place and then at the digit to the right.

    When rounding to the nearest hundredth, look at the digit in the hundredths place and then at the digit to the right.

    If the digit to the right of the digit you are rounding to is 4 or below, round down.

    If it is 5 or above, round up.

    For example, 8.4784 miles rounded to the nearest tenth would be 8.5 miles. This is because there is a 4 in the tenths place and a 7 to the right of this. 7 is 5 or above so we round up.

    8.4784 miles rounded to the nearest hundredth would be 8.48 miles. This is because there is a 7 in the hundredths place and an 8 to the right of this. 8 is 5 or above so we round up.

    Solution

    The car sets off from Kai's house to go to Luis' house 2.4376 miles away. Rounded to the nearest tenth, this is 2.4 miles away. They then continue to the service station which is 23.7845 miles from Luis' house. Rounded to the nearest hundredth, this is 23.78 miles.

    From here, the theme park is 37.6578 miles. Rounded to the nearest tenth, this is 37.7 miles.

    During the day, Kai and Luis walk 6.5598 miles around the park. Rounded to the nearest hundredth, this is 6.56 miles. They had a great day!