Decimals & Percents
Grades 4–7 Decimals Percents
The decimal point isn't a wall — it's just more place value. Every digit to the left is ×10 as you step left; every digit to the right is ÷10 as you step right. The places just keep going:
3 4 7 . 2 5 6
↑ ↑ ↑ ↑ ↑ ↑
100s 10s 1s 10ths 100ths 1000ths
So 347.256 = 300 + 40 + 7 + 2/10 + 5/100 + 6/1000. A decimal is a fraction whose denominator is a power of ten, written compactly.
Percents are hundredths
"Percent" literally means per cent — per hundred. 45% = 45/100 = 0.45. The conversion cycle is free movement between three outfits for the same number:
fraction decimal percent
3/4 → 0.75 → 75%
1/5 → 0.20 → 20%
7/8 → 0.875 → 87.5%
Everyday percent tricks
- 10% is the anchor. 10% of $36 = $3.60 (shift the point one place left). Then 20% = double it ($7.20), 5% = half it ($1.80), 15% = 10% + 5% ($5.40).
- Flip it. x% of y = y% of x. So 8% of 25 is the same as 25% of 8 — which is just 8 ÷ 4 = 2. Pick whichever direction is easier.
- 1% anchor. 1% of $450 = $4.50; multiply for anything — 7% = $31.50.
Decimals inside computers
Computers store decimals as binary "floating point" — and some decimals
you can write exactly (like 0.1) can't be stored exactly in binary,
which is why calculators and code sometimes show 0.1 + 0.2 =
0.30000000000000004. The two canonical references:
- Goldberg, D. (1991). What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys, 23(1), 5–48. doi:10.1145/103162.103163
- IEEE (2019). IEEE Standard for Floating-Point Arithmetic (IEEE 754-2019). doi:10.1109/IEEESTD.2019.8766229
Watch out
"Percent of" and "percentage points" are different things. An interest
rate rising from 4% to 5% went up 1 percentage point,
but 25 percent (of its old value). News reports mix
these constantly — now you won't.
Try it yourself:
- 15% of $80 (10% = 8, 5% = 4 → $12)
- 4% of 75 (flip: 75% of 4 → 3)
- Write 5/8 as a percent (0.625 → 62.5%)
Related: fractions · scientific notation for very big and very small numbers.