Dividing decimals by power of ten

Our number system is built on tens, so dividing by 10 makes every digit worth one place less. On paper that looks like the decimal point moving one place left for each zero, or for each unit of the exponent.

The page asks your child to write the divisor as a power first: 100 is 10², 1,000 is 10³. The exponent then says how many jumps the point makes. Item f, 0.00478 ÷ 10, checks that the rule still works for a number that already starts with zeros, and question a pushes it to six jumps.

The standards are 5.NBT.A.2, the Grade 5 pattern of the decimal point when dividing by a power of 10, and 6.NS.B.3.

Put a finger on the point in 20.153 and ask your child, "Divisor 10,000. How many zeros?" Four. Then hop the finger four places left, writing zeros where the digits run out.

That is where the likely slip happens. In item c, many kids stop at 0.20153, two hops short, because the digits seem to end there. Ask, "Did you hop four times?" and let them count again.

In the multiple-choice part, question b offers answers that share almost the same digits, 2.0153721 and 20.153721 among them. Your child can sort them by estimating the size of a quotient first: 20,153 ÷ 10,000 should be about 2.

Measure a table with a metric tape: 1,250 millimeters is 1.25 meters, a division by 1,000 your child can say out loud. Then read a food label in grams and turn it into kilograms the same way.

With money, ask what one tenth of a $57.20 grocery bill is. The digits stay, the point moves, and $5.72 appears.

Millions to Measure by David M. Schwartz walks through the metric system with Marvelosissimo the magician, and nearly every conversion in it is a power of ten.

Let your child hear what they did well: "You let the exponent count the jumps." The next sheet turns things around and divides whole numbers by decimals, where answers grow.