Powers of Ten: Homework

Multiplying by a power of ten moves the decimal point right. Dividing moves it left. The exponent says how far.

Part A — Move the Point / 10

Write the answer. Add zeros as placeholders when the point runs out of digits.

Each of these has a trap. Say which way the point moves and how far before you write.

1.
36 × 0.1. Does the point move right or left?Answer
2.
4.5 × 10^0. A student says the point moves zero places and writes 0. What is right?Answer
3.
0.052 × 10^2. Count the zeros in 100, not the digits in 0.052.Answer
4.
63 ÷ 1,000. Where do you need placeholder zeros?Answer
5.
Fill in the exponent: 7.2 × 10^? = 72,000.Answer

Real numbers. A U.S. $1 bill is 0.0043 inch thick, and a marathon is 42.195 kilometers.

Race	Kilometers
Marathon	42.195
Half marathon	21.0975

Think it through, then write your answer and one sentence about how you knew.

1.
Find the power of ten that turns 0.047 into 470. How many places does the point move, and which way?Answer
2.
Maya says 10^3 × 10^2 = 10^6 because 3 × 2 = 6. Check her by writing out 1,000 × 100. Is she right?Answer

Write your own, then work it.

1.
Write a decimal and a power of ten that turn it into a whole number when you multiply. Show the answer and say how many places the point moved.Answer

Total / 25

Graded by

Notes

Part A — the answers.

Part B — the answer.

3.6. Times 0.1 is the same as dividing by 10, so the point moves LEFT one place.
4.5. 10^0 equals 1, so nothing changes.
5.2
0.063. The point moves left three places, so a zero goes in front of the 6.
4. The point moves from 7.2 to 72,000, which is four places right.

Part C — the answers.

Part D — one correct answer, and what a good explanation says.

10^4. The point moves four places to the right: 0.047 to 0.47 to 4.7 to 47 to 470.
No. 1,000 × 100 = 100,000, which is 10^5. The exponents ADD: 3 + 2 = 5.

Part E — what a good problem looks like.

Answers vary. A good one matches the places to the exponent, such as 0.0072 × 10^4 = 72, where the point moves four places right.