1 · Decimal place value
In 3.472, the 4 is 4 tenths (0.4), the 7 is 7 hundredths (0.07), and the 2 is 2 thousandths (0.002).
Each place is ten times smaller than the place to its left, the same rule as whole numbers.
2 · Comparing and ordering decimals
Line up the decimal points and give every number the same number of places by adding zeros: 0.6, 0.58, 0.605 become 0.600, 0.580, 0.605.
Now compare like whole numbers: 580 < 600 < 605, so 0.58 < 0.6 < 0.605. More digits does not mean bigger: 0.58 has more digits than 0.6 but is smaller.
3 · Rounding decimals
Round 7.468 to the nearest tenth: the tenths digit is 4 and the digit after it is 6, so round up to 7.5.
Round 7.468 to the nearest hundredth: the hundredths digit is 6 and the next is 8, so 7.47. Chopping off digits (7.46) is not rounding.
4 · Adding and subtracting decimals
Line up the decimal points. 12.5 − 3.75: write 12.50 − 3.75 = 8.75.
With money, finish every step in dollars and cents. "Two books at $4.85 and a bookmark at $1.30, paid with $20": 9.70 + 1.30 = 11.00, and 20.00 − 11.00 = $9.00 change.
5 · Multiplying decimals
Multiply as if there were no decimal points, then count the decimal places in both numbers. 2.4 × 0.3: 24 × 3 = 72, and there are 2 decimal places in all, so 0.72.
Check with sense: 2.4 × 0.3 should be less than 2.4, because 0.3 is less than 1.
6 · Multiplying and dividing by 10, 100, 1,000
× 10 moves the decimal point one place right: 3.06 × 10 = 30.6. × 100 moves it two places: 3.06 × 100 = 306.
÷ moves it left: 45 ÷ 100 = 0.45, and 45 ÷ 1,000 = 0.045.
7 · Fractions, decimals, and percents
A percent is "out of 100": 35% = 35/100 = 0.35. A fraction becomes a decimal when you divide: 3/8 = 3 ÷ 8 = 0.375.
Learn the common ones: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%, 1/8 = 0.125 = 12.5%.
8 · Percent of a number
10% of a number is the number ÷ 10. So 10% of 80 is 8, 30% of 80 is 3 × 8 = 24, and 5% is half of 10%: 4.
Or use the fraction: 25% of 64 is 1/4 of 64 = 16.
9 · Sale prices
"A $60 jacket is 20% off." 20% of 60 is 12, the discount. The sale price is 60 − 12 = $48.
Read which one the question asks for. The discount and the sale price are both in the answer choices on purpose.
10 · Finding the whole from a percent
"20% of a number is 14. What is the number?" 20% is 1/5, so 1/5 of the number is 14, and the whole is 5 × 14 = 70.
Check: 20% of 70 = 14.
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