To express the number [tex]\(1.312 \times 10^2\)[/tex] in standard notation, we need to understand what this scientific notation means.
### Step-by-Step Solution
1. Understand the Components:
- The number [tex]\(1.312\)[/tex] is what we call the "coefficient" or "mantissa."
- The term [tex]\(10^2\)[/tex] indicates multiplying the coefficient by 10 raised to the power of 2.
2. Evaluate the Exponentiation:
- The exponent [tex]\(2\)[/tex] in [tex]\(10^2\)[/tex] means we multiply 10 by itself 2 times, which gives us 100.
3. Multiply the Coefficient by 100:
- Now we have [tex]\(1.312 \times 100\)[/tex].
- To perform this multiplication, shift the decimal point in 1.312 two places to the right (since multiplying by 100 is the same as moving the decimal point two places to the right).
4. Calculate the Result:
- So, [tex]\(1.312\)[/tex] becomes [tex]\(131.2\)[/tex].
Hence, the number [tex]\(1.312 \times 10^2\)[/tex] in standard notation is:
[tex]\[
131.20000000000002
\][/tex]
