Study notes

Decimals

Decimals up to 3 decimal places, comparing and rounding decimals, converting to fractions, and adding/subtracting decimals.

Learn it step by step

Decimal places show tenths, hundredths, thousandths

After the decimal point, each place has a value ten times smaller than the one before: tenths, hundredths, thousandths. In $4.325$ , the 3 is in the tenths place, the 2 is in the hundredths place, and the 5 is in the thousandths place.

4.325

sits just after

4

on the number line.

Compare decimals by lining up the decimal point

To compare $0.5$ and $0.15$ , write them with the same number of decimal places first: $0.50$ and $0.15$ . Now it is clear $0.50$ is bigger, even though 15 looks like a bigger number than 5.

0.5

is further along the number line than

0.15

Rounding a decimal looks at the next digit

To round $3.47$ to 1 decimal place, look at the hundredths digit, 7. Since $7 \geq 5$ , round the tenths digit up: $3.47$ rounds to $3.5$ .

Decimals and fractions describe the same amount

A decimal with 1 place is a number of tenths, and a decimal with 2 places is a number of hundredths: $0.7 = \frac{7}{10}$ and $0.35 = \frac{35}{100} = \frac{7}{20}$ .

0.35

is the same as

\frac{35}{100}

, 35 out of 100 squares shaded.

Add, subtract, multiply, and divide decimals like whole numbers

Line up the decimal points before adding or subtracting. To multiply or divide a decimal by a 1-digit whole number, work as usual and keep the decimal point in the matching position in the answer.

Worked examples

Write

6.08

in words using place value.

The whole number part is 6.
The tenths digit is 0 and the hundredths digit is 8.
$6.08 = 6$ ones and $8$ hundredths.

Which is bigger,

0.6

0.45

Write both to 2 decimal places: $0.60$ and $0.45$ .
Compare the tenths digit: 6 is bigger than 4.
$0.6$ is bigger.

Work out

5.6 + 3.75

Line up the decimal points, giving $5.60$ and $3.75$ .
Add as whole numbers: $560 + 375 = 935$ .
Place the decimal point back: $5.60 + 3.75 = 9.35$ .

Work out

7.2 \div 4

Divide as if there were no decimal point: $72 \div 4 = 18$ .
Place the decimal point in the same relative position.
$7.2 \div 4 = 1.8$ .

Mind map

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