For each of the following, give your answer in standard form.
(a) An external hard drive has a capacity of 4.0 terabytes. Given that 1 terabyte bytes,
express this capacity in bytes.
(b) The diameter of a human hair is 25.4 micrometres. Given that
1 micrometre metres, express this diameter in metres.
© A rain gauge measures rainfall over a period of time. The average annual rainfall in
Singapore is 2340 mm . Express this measurement in centimetres.

Ask by Huff Chang. in Singapore

Mar 24,2025

Question

For each of the following, give your answer in standard form.
(a) An external hard drive has a capacity of 4.0 terabytes. Given that 1 terabyte bytes,
express this capacity in bytes.
(b) The diameter of a human hair is 25.4 micrometres. Given that
1 micrometre metres, express this diameter in metres.
© A rain gauge measures rainfall over a period of time. The average annual rainfall in
Singapore is 2340 mm . Express this measurement in centimetres.

Ask by Huff Chang. in Singapore

Mar 24,2025

UpStudy AI · Accepted Answer

**(a)**  
The external hard drive has a capacity of $$ 4.0 $$ terabytes. Since  
$$
1 \text{ terabyte} = 10^{12} \text{ bytes},
$$  
we multiply:  
$$
4.0 \text{ TB} = 4.0 \times 10^{12} \text{ bytes}.
$$

**(b)**  
The diameter of a human hair is given as $$ 25.4 $$ micrometres. Since  
$$
1 \text{ micrometre} = 10^{-6} \text{ metres},
$$  
we have:  
$$
25.4 \text{ µm} = 25.4 \times 10^{-6} \text{ m}.
$$  
Expressing $$ 25.4 $$ in scientific notation gives:
$$
25.4 = 2.54 \times 10^1,
$$  
thus:
$$
25.4 \times 10^{-6} = (2.54 \times 10^1) \times 10^{-6} = 2.54 \times 10^{-5} \text{ m}.
$$

**(c)**  
The average annual rainfall is $$ 2340 $$ millimetres. Since  
$$
1 \text{ centimetre} = 10 \text{ millimetres},
$$  
we convert by dividing by 10:  
$$
2340 \text{ mm} = \frac{2340}{10} \text{ cm} = 234 \text{ cm}.
$$  
In standard scientific form, $$ 234 $$ can be written as:
$$
234 = 2.34 \times 10^2,
$$  
so the rainfall is:
$$
2.34 \times 10^2 \text{ cm}.
$$
**(a)** 4.0 terabytes is $$ 4.0 \times 10^{12} $$ bytes. **(b)** 25.4 micrometres is $$ 2.54 \times 10^{-5} $$ metres. **(c)** 2340 millimetres is $$ 2.34 \times 10^{2} $$ centimetres.

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