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Guided Practice

Complete each equation to write 30,000 in scientific notation in the final equation.

30,000 =  30,000   ×    100

30,000 = × 101

30,000 = 300       ×       10

30,000 = 30          ×       10

30,000 = ×  10

Complete each equation to write 134,600 in scientific notation in the final equation.

134,600 = ×  101

134,600 = 1,346      ×      10

134,600 = 134.6        ×     10

134,600 = 13.46        ×     10

134,600 = ×  10

Complete each equation to write 0.000315 in scientific notation in the final equation.

0.000315 = 0.000315  ×  100

0.000315 = × 10–1

0.000315 = 0.0315     ×     10

0.000315 = 0.315       ×      10

0.000315 = ×  10

Complete each equation to write 0.002997 in scientific notation in the final equation.

0.002997 = 0.002997   ×   100

0.002997 =  ×   10–1

0.002997 = 0.2997      ×     10

0.002997 =  ×   10

Write the number 45,620 in scientific notation.

45,620 = × 10

Write the number 8,110,294,407 in scientific notation.

8,110,294,407 = × 10

Write the number 6,926,000 in scientific notation.

6,926,000 = × 10

Write the number 0.000849 in scientific notation.

0.000849 = × 10

Write the number 0.62 in scientific notation.

0.62 = × 10

Write the number 0.00004 in scientific notation.

0.00004 = × 10

Write the number 4.3 × 106 in standard form as a decimal.

4.3 × 106 =

Write the number 6.12 × 107 in standard form as a decimal.

6.12 × 107 =

Write the number 4.22 × 10–2 in standard form as a decimal.

4.22 × 10–2 =

Write the number 9.945 × 10–6 in standard form as a decimal.

9.945 × 10–6 =

Write the number 5.5 × 10–9 in standard form as a decimal.

5.5 × 10–9 =

Write the exponent used in the scientific notation of a number in the:

thousands : 3

hundred thousands:

millions:   

billions:   

How does 7.5 × 104 compare to 1.5 × 109?

We know that 109 is 105 times (100,000 times) 104, because 109 ÷ 104 is 109 – 4 = 105. And 1.5 is 1/5 times 7.5, because 1.5 ÷ 7.5 is 1/5.

So, 1.5 × 109 is 1/5 × 105 times, or 20,000 times, the value of 7.5 × 104.

To compare two numbers in scientific notation,
a × 10m and b × 10n, you can use a ratio:

Write the answer as a ratio of two integers.

7.5 × 104 is / times the
value of 1.5 × 109.

Write the answer as a ratio of two integers.

2.84 × 10–4 is / times the
value of 1.42 × 10–5.

Write the answer as a ratio of two integers.

7.004 × 109 is / times the
value of 1.751 × 1010.

Write the answer as a ratio of two integers.

5.59 × 10–2 is / times the
value of 19.565 × 102.

Write the answer as a ratio of two integers.

1.0422 × 107 is / times the
value of 9.3798 × 106.

Write the answer as a ratio of two integers.

6.04 × 103 is / times the value of 1.51 × 10–2.

Write the answer as a ratio of two integers.

8.96 × 10–3 is / times the
value of 1.12 × 102.

Write the answer as a ratio of two integers.

9.001 × 106 is / times the
value of 1.8002 × 107.

Write the answer as a ratio of two integers.

1.5066 × 104 is / times the value of 3.0132 × 10–4.

To add or subtract numbers in scientific notation, you can change one of the numbers so it has the same exponent as the other. For example, determine the sum 2.05 × 105 + 9.11 × 104.

9.11 × 104 = 0.911 × 105

So, 2.05 × 105 + 0.911 × 105 = 2.961 × 105.

Write the sum or difference. The result does not have to be written in scientific notation.

6.64 × 103 + 2.005 × 105 = × 10

Write the sum or difference. The result does not have to be written in scientific notation.

7.03 × 10–2 – 1.66 × 102 = × 10

Write the sum or difference. The result does not have to be written in scientific notation.

4.35 × 109 + 9.62 × 105 = × 10

Write the sum or difference. The result does not have to be written in scientific notation.

8.904 × 10–1 – 7.0 × 102 = × 10

Write the sum or difference. The result does not have to be written in scientific notation.

5.56 × 108 – 1.09 × 103 = × 10