Question

Write out the following numbers in full with the correct number of zeros: (a)\({\bf{8}}{\bf{.69 \times 1}}{{\bf{0}}^{\bf{4}}}\), (b)\({\bf{9}}{\bf{.1 \times 1}}{{\bf{0}}^{\bf{3}}}\), (c)\({\bf{8}}{\bf{.8 \times 1}}{{\bf{0}}^{{\bf{ - 1}}}}\), (d)\({\bf{4}}{\bf{.76 \times 1}}{{\bf{0}}^{\bf{2}}}\), and (e)\({\bf{3}}{\bf{.62 \times 1}}{{\bf{0}}^{{\bf{ - 5}}}}\).

Short answer

The given numbers in full with the correct number of zeros are (a) 86900, (b) 9100, (c) 0.88, (d) 476, and (e) 0.0000362.

Step-by-step solution

Writing the numbers in full with the correct count of zeros

The correct way to express the number of zeros is to multiply the powers of 10 directly with the decimal number. The powers of 10 are used before the multiplication operator in the same number.

For example, the number \(7.89 \times {10^5}\) can be written in full as \(789000\).

(a) Conversion of the number \({\bf{8}}{\bf{.69 \times 1}}{{\bf{0}}^{\bf{4}}}\) in full with the correct count of zeros 

Thenumber\(8.69 \times {10^4}\)can be written in fullas

\(\begin{aligned}{c}8.69 \times {10^4} = 8.69 \times 10000\\ = 86900.\end{aligned}\)

Thus,\(8.69 \times {10^4}\)can be written in full with the correct count of zeros as\(86900\).

(b) Conversion of the number \({\bf{9}}{\bf{.1 \times 1}}{{\bf{0}}^{\bf{3}}}\) in full with the correct count of zeros

Thenumber\(9.1 \times {10^3}\)can be written in full as

\(\begin{aligned}{c}9.1 \times {10^3} = 9.1 \times 1000\\ = 9100.\end{aligned}\)

Thus, \(9.1 \times {10^3}\) can be written in full with the correct count of zeros as \(9100\).

(c) Conversion of the number \({\bf{8}}{\bf{.8 \times 1}}{{\bf{0}}^{{\bf{ - 1}}}}\) in full with the correct count of zeros 

Thenumber\(8.8 \times {10^{ - 1}}\)can be written in full as

\(\begin{aligned}{c}8.8 \times {10^{ - 1}} = 8.8 \times \frac{1}{{10}}\\ = 0.88.\end{aligned}\)

Thus, \(8.8 \times {10^{ - 1}}\) can be written in full with the correct count of zeros as \(0.88\).

(d) Conversion of the number \({\bf{4}}{\bf{.76 \times 1}}{{\bf{0}}^{\bf{2}}}\) in full with the correct count of zeros

Thenumber\(4.76 \times {10^2}\)can be written in full as

\(\begin{aligned}{c}4.76 \times {10^2} = 4.76 \times 100\\ = 476.\end{aligned}\)

Thus, \(4.76 \times {10^2}\) can be written in full with the correct count of zeros as \(476\).

(e) Conversion of the number \({\bf{3}}{\bf{.62 \times 1}}{{\bf{0}}^{{\bf{ - 5}}}}\) in full with the correct count of zeros.

Thenumber\(3.62 \times {10^{ - 5}}\)can be written in full as

\(\begin{aligned}{c}3.62 \times {10^{ - 5}} = 3.62 \times \frac{1}{{100000}}\\ = 0.0000362.\end{aligned}\)

Thus,\(3.62 \times {10^{ - 5}}\)can be written in full with the correct count of zeros as\(0.0000362\).