Sure! Let's convert the number 9974 into scientific notation step-by-step.
1. Identify the significant figures:
We need to express 9974 with a single non-zero digit to the left of the decimal point. In this case, 9974 can be written as 9.974. This number still represents the same quantity but in a different form.
2. Count the decimal places moved:
To transform 9974 into 9.974, we have effectively moved the decimal point 3 places to the left. Each move of the decimal point to the left increases the exponent of 10 by 1.
3. Combine the significant figure with the power of 10:
Since we moved the decimal point 3 places to the left, we multiply 9.974 by [tex]\(10^3\)[/tex].
4. Round to the appropriate number of significant figures:
Typically, scientific notation retains a meaningful number of significant figures based on the precision of the original number. Here, we round 9.974 to two decimal places, which gives us 9.97.
Therefore, 9974 written in scientific notation is:
[tex]\[ 9.97 \times 10^3 \][/tex]
