Answer :
Certainly! Here are the step-by-step calculations for each of the given expressions, providing the answers to an appropriate degree of accuracy:
(a) [tex]\(23.456 \times 17.89\)[/tex]:
We start by multiplying the numbers and then round the result to two decimal places, which is common for multiplication involving large numbers.
[tex]\[ 23.456 \times 17.89 = 419.63 \][/tex]
So, [tex]\(23.456 \times 17.89 = 419.63\)[/tex].
(b) [tex]\(0.4 \times 12.62\)[/tex]:
Next, we multiply these numbers and round the answer to two decimal places.
[tex]\[ 0.4 \times 12.62 = 5.05 \][/tex]
Thus, [tex]\(0.4 \times 12.62 = 5.05\)[/tex].
(c) [tex]\(18 \times 9.24\)[/tex]:
We perform the multiplication and round the results to two decimal places.
[tex]\[ 18 \times 9.24 = 166.32 \][/tex]
Therefore, [tex]\(18 \times 9.24 = 166.32\)[/tex].
(d) [tex]\(76.24 \div 3.2\)[/tex]:
We divide these numbers and round the result to two decimal places.
[tex]\[ 76.24 \div 3.2 = 23.82 \][/tex]
Hence, [tex]\(76.24 \div 3.2 = 23.82\)[/tex].
(e) [tex]\(7.6^2\)[/tex]:
We calculate the square of the number and round to two decimal places.
[tex]\[ 7.6^2 = 57.76 \][/tex]
So, [tex]\(7.6^2 = 57.76\)[/tex].
(f) [tex]\(16.42^3\)[/tex]:
We cube the number, which typically is rounded to three decimal places for cubic values.
[tex]\[ 16.42^3 = 4427.101 \][/tex]
Thus, [tex]\(16.42^3 = 4427.101\)[/tex].
(g) [tex]\(\frac{2.3 \times 3.37}{4}\)[/tex]:
We first multiply the numbers in the numerator and then divide by 4, rounding the result to three decimal places.
[tex]\[ \frac{2.3 \times 3.37}{4} = 1.938 \][/tex]
Therefore, [tex]\(\frac{2.3 \times 3.37}{4} = 1.938\)[/tex].
(h) [tex]\(\frac{8.31}{2.02}\)[/tex]:
We divide these numbers and round the result to three decimal places.
[tex]\[ \frac{8.31}{2.02} = 4.114 \][/tex]
Hence, [tex]\(\frac{8.31}{2.02} = 4.114\)[/tex].
(i) [tex]\(9.2 \div 4^2\)[/tex]:
We first calculate [tex]\(4^2\)[/tex] and then divide 9.2 by this result, rounding to two decimal places.
[tex]\[ 4^2 = 16 \][/tex]
[tex]\[ 9.2 \div 16 = 0.57 \][/tex]
Thus, [tex]\(9.2 \div 4^2 = 0.57\)[/tex].
In summary:
1. [tex]\(23.456 \times 17.89 = 419.63\)[/tex]
2. [tex]\(0.4 \times 12.62 = 5.05\)[/tex]
3. [tex]\(18 \times 9.24 = 166.32\)[/tex]
4. [tex]\(76.24 \div 3.2 = 23.82\)[/tex]
5. [tex]\(7.6^2 = 57.76\)[/tex]
6. [tex]\(16.42^3 = 4427.101\)[/tex]
7. [tex]\(\frac{2.3 \times 3.37}{4} = 1.938\)[/tex]
8. [tex]\(\frac{8.31}{2.02} = 4.114\)[/tex]
9. [tex]\(9.2 \div 4^2 = 0.57\)[/tex]
(a) [tex]\(23.456 \times 17.89\)[/tex]:
We start by multiplying the numbers and then round the result to two decimal places, which is common for multiplication involving large numbers.
[tex]\[ 23.456 \times 17.89 = 419.63 \][/tex]
So, [tex]\(23.456 \times 17.89 = 419.63\)[/tex].
(b) [tex]\(0.4 \times 12.62\)[/tex]:
Next, we multiply these numbers and round the answer to two decimal places.
[tex]\[ 0.4 \times 12.62 = 5.05 \][/tex]
Thus, [tex]\(0.4 \times 12.62 = 5.05\)[/tex].
(c) [tex]\(18 \times 9.24\)[/tex]:
We perform the multiplication and round the results to two decimal places.
[tex]\[ 18 \times 9.24 = 166.32 \][/tex]
Therefore, [tex]\(18 \times 9.24 = 166.32\)[/tex].
(d) [tex]\(76.24 \div 3.2\)[/tex]:
We divide these numbers and round the result to two decimal places.
[tex]\[ 76.24 \div 3.2 = 23.82 \][/tex]
Hence, [tex]\(76.24 \div 3.2 = 23.82\)[/tex].
(e) [tex]\(7.6^2\)[/tex]:
We calculate the square of the number and round to two decimal places.
[tex]\[ 7.6^2 = 57.76 \][/tex]
So, [tex]\(7.6^2 = 57.76\)[/tex].
(f) [tex]\(16.42^3\)[/tex]:
We cube the number, which typically is rounded to three decimal places for cubic values.
[tex]\[ 16.42^3 = 4427.101 \][/tex]
Thus, [tex]\(16.42^3 = 4427.101\)[/tex].
(g) [tex]\(\frac{2.3 \times 3.37}{4}\)[/tex]:
We first multiply the numbers in the numerator and then divide by 4, rounding the result to three decimal places.
[tex]\[ \frac{2.3 \times 3.37}{4} = 1.938 \][/tex]
Therefore, [tex]\(\frac{2.3 \times 3.37}{4} = 1.938\)[/tex].
(h) [tex]\(\frac{8.31}{2.02}\)[/tex]:
We divide these numbers and round the result to three decimal places.
[tex]\[ \frac{8.31}{2.02} = 4.114 \][/tex]
Hence, [tex]\(\frac{8.31}{2.02} = 4.114\)[/tex].
(i) [tex]\(9.2 \div 4^2\)[/tex]:
We first calculate [tex]\(4^2\)[/tex] and then divide 9.2 by this result, rounding to two decimal places.
[tex]\[ 4^2 = 16 \][/tex]
[tex]\[ 9.2 \div 16 = 0.57 \][/tex]
Thus, [tex]\(9.2 \div 4^2 = 0.57\)[/tex].
In summary:
1. [tex]\(23.456 \times 17.89 = 419.63\)[/tex]
2. [tex]\(0.4 \times 12.62 = 5.05\)[/tex]
3. [tex]\(18 \times 9.24 = 166.32\)[/tex]
4. [tex]\(76.24 \div 3.2 = 23.82\)[/tex]
5. [tex]\(7.6^2 = 57.76\)[/tex]
6. [tex]\(16.42^3 = 4427.101\)[/tex]
7. [tex]\(\frac{2.3 \times 3.37}{4} = 1.938\)[/tex]
8. [tex]\(\frac{8.31}{2.02} = 4.114\)[/tex]
9. [tex]\(9.2 \div 4^2 = 0.57\)[/tex]
