Sure! Let's work through each part of the question step-by-step.
### Part (a):
To write [tex]\( 7.1 \times 10^{-2} \)[/tex] as an ordinary number, we need to understand what multiplying by [tex]\( 10^{-2} \)[/tex] does. The exponent [tex]\( -2 \)[/tex] means that we move the decimal point two places to the left.
Starting with 7.1:
- 7.1
Moving the decimal point two places to the left:
- 0.071
So, [tex]\( 7.1 \times 10^{-2} \)[/tex] as an ordinary number is 0.071.
### Part (b):
To work out the value of [tex]\( (6.8 \times 10^2) \times (1.3 \times 10^{-3}) \)[/tex] and give the answer in standard form, we need to use the properties of exponents and multiplication.
1. First, multiply the numerical coefficients (the numbers without the exponents):
[tex]\[
6.8 \times 1.3 = 8.84
\][/tex]
2. Next, add the exponents of 10:
[tex]\[
10^2 \times 10^{-3} = 10^{2 + (-3)} = 10^{-1}
\][/tex]
3. Combine the results of the two steps:
[tex]\[
(6.8 \times 10^2) \times (1.3 \times 10^{-3}) = 8.84 \times 10^{-1}
\][/tex]
So, the value of [tex]\( (6.8 \times 10^2) \times (1.3 \times 10^{-3}) \)[/tex] in standard form is [tex]\( 8.84 \times 10^{-1} \)[/tex].
Therefore, the detailed solutions are:
a) [tex]\( 7.1 \times 10^{-2} = 0.071 \)[/tex]
b) [tex]\( (6.8 \times 10^2) \times (1.3 \times 10^{-3}) = 8.84 \times 10^{-1} \)[/tex]
