Decimal place value chart

What the chart shows

This chart has columns from thousands down to ten-thousandths, with the decimal point fixed between the ones and the tenths. Pick a number, such as 3.457, and its digits sit in colored tiles in their columns. Tap a digit to see its value. The buttons multiply or divide by 10, 100 or 1,000, and the digits slide left or right across the columns while the decimal point stays still. Faded zeros appear wherever a place holder is needed, such as the 0 in 0.35 or in 40.7.

Why sliding digits helps

Many children learn "move the decimal point" for multiplying by 10. It gets the right answer but hides what is happening. Every digit becomes worth ten times as much, so each one moves one place to the left, while the point stays between the ones and the tenths. Seeing the tiles slide makes that visible, and it explains why the same thing happens with whole numbers: 407 × 10 = 4,070 because 4 hundreds become 4 thousands, not because a zero is stuck on the end.

Common mix-ups

• Adding a zero to multiply by 10. That works for 407, but 3.4570 is still 3.457. Sliding the digits gives the correct 34.57.
• Thinking the decimal point does the moving. On the chart, the point never moves; the digits do, which is what changes their values.
• Reading 0.035 as bigger than 0.6 because 35 is bigger than 6. Tap the digits: the 3 in 0.035 is 3 hundredths, while the 6 in 0.6 is 6 tenths.
• Leaving out place-holder zeros. 4.07 and 4.7 are different numbers; the 0 holds the empty tenths place.

A 10-minute activity

• Minutes 1 to 3: choose 3.457 and tap each digit. The child says its value in words and as a decimal.
• Minutes 4 to 6: press × 10 and ask what happened to the 4. It was 4 tenths and is now 4 ones. Press ÷ 10 to bring it back.
• Minutes 7 to 8: choose 0.6 and divide by 100. Ask why the answer, 0.006, needs zeros in the tenths and hundredths places.
• Minutes 9 to 10: press Challenge and try to reach the target in one move. The child says the multiplication or division out loud before pressing it.

Where it fits by grade

• Grade 4: decimal notation for tenths and hundredths (Common Core 4.NF.C.6), and the whole-number idea that a digit is worth ten times as much as it would be in the place to its right (4.NBT.A.1).
• Grade 5: the same idea for decimals (5.NBT.A.1), patterns when multiplying and dividing by powers of 10 (5.NBT.A.2), and reading, writing and comparing decimals to thousandths (5.NBT.A.3).
• Grade 6: fluent decimal arithmetic, which leans on these patterns.
• England: Year 4 pupils divide one- and two-digit numbers by 10 and 100 and name the digits in the answer as ones, tenths and hundredths, Year 5 pupils multiply and divide whole numbers and decimals by 10, 100 and 1,000, and Year 6 pupils work with numbers to three decimal places.

Learning more

Place value and multiplying and dividing decimals are both skills on Eurekami's skill map. Lessons use place value charts like this one when a question needs them, and Daily Practice brings these skills back when they start to slip.