ArithmeticBeginner

Decimals Explained

A decimal is just another way to write a fraction whose denominator is a power of 10. The decimal point separates the whole number part from the fractional part. Everything to the right of the decimal point represents parts of one whole.

✔ Quick Answer

Decimals use place value: 0.1 means one tenth, 0.01 means one hundredth, 0.001 means one thousandth. The number 3.47 means 3 wholes, 4 tenths, and 7 hundredths. To convert a fraction to a decimal, divide the numerator by the denominator.

1 Place Value and What Each Digit Means

Every digit in a decimal has a position that tells you its value. Moving left from the decimal point: ones, tens, hundreds. Moving right: tenths, hundredths, thousandths.

Place value in 4,827.365
4Thousands , worth 4,000
8Hundreds , worth 800
2Tens , worth 20
7Ones , worth 7
.Decimal point , separates whole and fractional parts
3Tenths , worth 3/10 = 0.3
6Hundredths , worth 6/100 = 0.06
5Thousandths , worth 5/1000 = 0.005

2 Converting Between Fractions and Decimals

Fraction to decimal: divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. 1/3 = 1 ÷ 3 = 0.333... (repeating).

Decimal to fraction: read the place value of the last digit and write the fraction. 0.4 = 4/10 = 2/5. 0.35 = 35/100 = 7/20. 0.125 = 125/1000 = 1/8.

Common conversions to memorize

1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/3 = 0.333..., 2/3 = 0.666..., 1/5 = 0.2, 1/8 = 0.125, 1/10 = 0.1. These appear constantly , knowing them by heart saves time.

3 Adding and Subtracting Decimals

Line up the decimal points, then add or subtract as normal. Trailing zeros can be added to make alignment easier without changing the value.

Adding Decimals
Calculate 12.6 + 3.47
1Line up decimal points: 12.60 + 3.47 (add trailing zero)
2Add column by column right to left: 0+7=7, 6+4=10 (write 0 carry 1), 2+3+1=6, 1+0=1
3Result: 16.07
Answer: 16.07

4 Multiplying Decimals

Ignore decimal points, multiply as whole numbers, then count the total decimal places in both factors and place the point in the answer.

Multiplying Decimals
Calculate 2.4 × 1.5
1Ignore decimals: 24 × 15 = 360
2Count decimal places: 2.4 has 1, 1.5 has 1, total = 2
3Place point 2 places from right: 3.60 = 3.6
Answer: 3.6

5 Dividing Decimals

Move the decimal point in the divisor to make it a whole number, move the dividend's decimal the same number of places, then divide normally.

Dividing Decimals
Calculate 4.8 ÷ 0.6
1Move decimal in divisor (0.6) one place right: becomes 6
2Move decimal in dividend (4.8) one place right: becomes 48
3Divide: 48 ÷ 6 = 8
Answer: 8
Misplacing the decimal in multiplication

2.3 × 4.1: some students write 94.3 instead of 9.43. Count decimal places carefully: 1 + 1 = 2 places, so the answer has 2 decimal places.

Practice Problems

Convert 5/8 to a decimal
5 ÷ 8 = 0.625
Add: 7.83 + 2.9
7.83 + 2.90 = 10.73
Multiply: 3.2 × 2.5
32 × 25 = 800. Two decimal places total: 8.00 = 8
Divide: 9.6 ÷ 0.4
Move decimal: 96 ÷ 4 = 24