Place Value × 10 and ÷ 10
Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left
What a learner can do afterwards
- Explain that the 4 in 0.04 is 1/10 of the 4 in 0.4
- State that a digit moving one place left is ×10 and one place right is ÷10
- Compare the value of the 6 in 6,000 and in 0.006
1 · Read
You already know a digit's value changes when it moves places in a whole number. That same rule keeps going past the ones place, right through the decimal point. Move a digit one place to the left, and it is worth 10 times as much. Move it one place to the right, and it is worth 10 times less.
Look at 0.4. The 4 sits in the tenths place, worth 4 tenths. Now look at 0.04. The 4 sits one place to the right, in the hundredths place. It moved right, so its value divided by 10: 4 tenths divided by 10 is 4 hundredths.
Remember: the decimal point never moves. Digits slide past it, growing ten times bigger to the left and ten times smaller to the right.
A digit's value is always ten times its neighbor one place to the right, and one tenth of its neighbor one place to the left.
More to read
Decimal place value review
Decimal places run tenths, hundredths, thousandths to the right of the point. In 87.654, the 8 is tens, the 7 is ones, then 6 tenths, 5 hundredths, 4 thousandths. Each step right is 1/10 of the last: the 4 in 0.04 is 1/10 of the 4 in 0.4. Each step left multiplies by 10: a digit moving one place left grows ten times. Compare digits by place, not by looks: the 6 in 6,000 dwarfs the 6 in 0.006 because thousands sit six steps left of thousandths.
Key ideas: multiply a two-digit multiple of 10 by a two-digit multiple of 10
Zeros tag along when tens multiply. Hide them, multiply the facts, bring them back. 30 x 40 hides to 3 x 4 = 12, then two zeros return: 1200. The same shift rule moves digits: 35 x 10 slides every digit one place left to make 350, and 4,200 / 10 slides right to make 420. Count zeros in, count zeros out. Place value never blinks: left is times ten, right is divide by ten.
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2 · Watch
به انگلیسیTake it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
14 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.