Patterns with Exponents and Powers of 10
7 x 101 =
7 x 102 =
7 x 103 =
7 x 104 =
70, 700, 7,000, 70,000
Write 10,000 + 20 + 3 in standard form.
10,023
873/1000
written as a decimal is
0.873
Write 425.52 in word form.
Four hundred twenty-five and fifty-two hundredths
Compare the decimal using >,< or =
0.890 _ 0.89
0.890 = 0.89
Round 34.731 to the nearest whole number.
35
Why are there three zeros in the product of 6 x 103?
Since the exponent on power of 10 is 3, there are 3 zeros in the product
Write 85,000,011 in expanded form.
(8 x 10,000,000)+ (5 x 1,000,000) + (1 x 10) + (1 x 1) or
(8 x 107) +(5 x 106) + (1 x 101) + (1 x 1)
0.007 written as a fraction is
7/1000
Write two decimals equivalent to 8.1
8.10, 8.100
Compare the decimal using >,< or =
9.707 _ 9.717
9.707< 9.717
Round 6.4382 to the nearest hundredth.
6.44
Susan said that 105 is 50. What mistake did Susan make? What is the correct answer?
Sample answer: She multiplied 10 by 5 rather than multiplying 10 five times; 100,000.
In 9,290 is the value of the first 9 ten times as great as the value of the second 9? Explain.
Sample answer:
No. Since the 9s are not next to each other in the number the first 9 is not 10 times the value of the second 9.
0.3 is 10 times as great as what decimal? 0.003 is 1/10 of what decimal?
0.03, 0.03
The number 3.453 has two 3s. Why does each 3 have a different value?
The first 3 is in the ones place, the second 3 is in the thousandths place.
Order the decimals from least to greatest: 5.540, 5.625, 5.631
5.540, 5.625, 5.631
A car rental service charges customers for the number of miles they travel, rounded to the nearest whole mile. George travels 40.8 miles. For how many miles will he be charged? Explain.
41 miles, 40.8 rounds to 41 when rounded to the nearest whole number.
George said that 6 x 103 is 180. Do you agree or disagree? If you disagree, explain the mistake that he made and find the correct answer.
Sample answer: George multiplied 6 x 10 by the exponent 3 to get 180 rather than multiplying 6 by the product (10x10x10). The correct answer is 6,000.
Paul says that in the number 6,367, one 6 is 10 times as great as the other 6. Is he correct? Explain why or why not.
Sample answer:
No, The 6s are not next to each other. The 6 in the thousands place is 100 times greater than the 6 in the tens place.
0.04 is 10 times as great as which decimal?
0.004
Write this number in standard form 4 x 100 +7 x 10 + 6 x 1 + 6 x (1/10) + 3 x (1/100) + 7 x (1/1000)
476.637
Order the decimals from greatest to least: 435.566, 436.565, 435.665
436.565, 435.665, 435.566
Name two different numbers that round to 8.21 when rounded to the nearest hundredth.
Sample answer: 8.213, 8.209
Santiago hopes to buy a 4 horse trailer for about $12,000. Describe all the numbers that when rounded to the nearest hundred are 12,000.
Sample answer:
Numbers greater than or equal to 11,950 and less than 12,050.
Colleen says she is thinking of a 4-digit number in which all the digits are the same. The value of the digit in the hundreds place is 200. What is the number? Explain.
Sample answer: 2,222; The digit in the hundreds place is 2 since its value is 200, Since one digit is 2, all the digits are 2.
Kelly said that 97/1000 can be written as 0.97. Is she correct? Explain.
Sample answer: No. 97/1000 is equivalent to 0.097. 0.97 is equivalent to 97/100
Cheryl’s softball batting average is 0.340, and Karin’s is 0.304. Karin says they have the same average. What error did she make? Explain.
They have different averages. Cheryl’s average is 0.300 + 0.040. Karin’s is 0.300 + 0.004.
Cara weighed some apples at the grocery store. The apples weighed 4.16 pounds. Which numbers are greater than 4.16?
4.15, 4.19, 4.2, 4.09, 4.1
4.19
4.2
Emma needs 2 pounds of ground meat to make a meatloaf. She has one package with 2.36 pounds of ground meat and another package with 2.90 pounds of ground meat. She uses rounding and finds that both packages are close to 2 pounds. Explain how Emma can choose the package closer to 2 pounds.
Sample answer: Look at the digit in the tenths place. 0 is less than 3 so 2.09 is closer to 2.