Guided Practice

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

30,000 = 30,000 × 10^{0}

30,000 = × 10^{1}

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 = × 10^{1}

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 × 10^{0}

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 × 10^{0}

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 × 10^{6} in standard form as a decimal.

4.3 × 10^{6} =

Write the number 6.12 × 10^{7} in standard form as a decimal.

6.12 × 10^{7} =

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 × 10^{4} compare to 1.5 × 10^{9}?

We know that 10^{9} is 10^{5} times (100,000 times) 10^{4}, because 10^{9} ÷ 10^{4} is 10^{9 – 4} = 10^{5}. And 1.5 is 1/5 times 7.5, because 1.5 ÷ 7.5 is 1/5.

So, 1.5 × 10^{9} is 1/5 × 10^{5} times, or 20,000 times, the value of 7.5 × 10^{4}.

To compare two numbers in scientific notation,

a × 10^{m} and b × 10^{n}, you can use a ratio:

Write the answer as a ratio of two integers.

7.5 × 10^{4} is / times the

value of 1.5 × 10^{9}.

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 × 10^{9} is / times the

value of 1.751 × 10^{10}.

Write the answer as a ratio of two integers.

5.59 × 10^{–2} is / times the

value of 19.565 × 10^{2}.

Write the answer as a ratio of two integers.

1.0422 × 10^{7} is / times the

value of 9.3798 × 10^{6}.

Write the answer as a ratio of two integers.

6.04 × 10^{3} 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 × 10^{2}.

Write the answer as a ratio of two integers.

9.001 × 10^{6} is / times the

value of 1.8002 × 10^{7}.

Write the answer as a ratio of two integers.

1.5066 × 10^{4} 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 × 10^{5} + 9.11 × 10^{4}.

9.11 × 10^{4} = 0.911 × 10^{5}

So, 2.05 × 10^{5} + 0.911 × 10^{5} = 2.961 × 10^{5}.

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

6.64 × 10^{3} + 2.005 × 10^{5} = × 10

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

7.03 × 10^{–2} – 1.66 × 10^{2} = × 10

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

4.35 × 10^{9} + 9.62 × 10^{5} = × 10

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

8.904 × 10^{–1} – 7.0 × 10^{2} = × 10

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

5.56 × 10^{8} – 1.09 × 10^{3} = × 10