Decimals
Thousandths & Decimal–Fraction Conversion
The third place after the decimal point is thousandths (0.001 = 1/1000). In 2.345 there are 2 ones, 3 tenths, 4 hundredths and 5 thousandths.
To change a decimal to a fraction, write the digits over 10, 100 or 1000: 0.25 = 25/100 = ¼. To change a fraction to a decimal, make the denominator 10, 100 or 1000: ¾ = 75/100 = 0.75.
- Third decimal place = thousandths (0.001 = 1/1000).
- Decimal to fraction: digits over 10/100/1000.
Comparing & Ordering Decimals
To compare decimals, line them up by place and compare the whole numbers first, then tenths, then hundredths, then thousandths. Adding zeros helps: 0.5 = 0.50.
So 0.5 is greater than 0.45, and to order 0.3, 0.33 and 0.303 from least we write 0.3, 0.303, 0.33.
- Compare wholes, then tenths, hundredths, thousandths.
- Add zeros to give the same number of places (0.5 = 0.50).
Multiplying & Dividing by 10, 100, 1000
Multiplying a decimal by 10, 100 or 1000 moves the decimal point to the right by 1, 2 or 3 places. Dividing moves it to the left by 1, 2 or 3 places.
So 2.5 × 10 = 25, and 45 ÷ 100 = 0.45.
- × 10/100/1000: move the point right 1/2/3 places.
- ÷ 10/100/1000: move the point left 1/2/3 places.