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.
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.
In this lesson
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.
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.
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.
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.
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.
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.