What is 0.00784 rounded to 2 significants figures?
The Correct Answer and Explanation is:
The number 0.00784 rounded to two significant figures is 0.0078.
Explanation:
When rounding a number to a specific number of significant figures, the goal is to maintain the precision of the number while eliminating any unnecessary digits. Significant figures are the digits in a number that carry meaningful information about its precision. This includes all non-zero digits, any zeros between significant digits, and any trailing zeros in a decimal number.
Step 1: Identify the Significant Figures
The number in question is 0.00784. To identify its significant figures, we first need to locate the decimal point and count the digits that contribute to the precision of the number. Here’s how we break it down:
- The 0.00784 has leading zeros, which are not considered significant figures because they only serve to position the decimal point. We start counting significant figures from the first non-zero digit, which in this case is 7.
- The digits 7, 8, and 4 are the significant figures. So, we have three significant figures in the number 0.00784.
Step 2: Round the Number
We need to round this number to two significant figures. This means we keep the first two digits of the number and round the remaining digits accordingly.
- The first two significant digits are 7 and 8, so we keep these.
- The third significant digit is 4, and since 4 is less than 5, we do not round up the second digit. Thus, we leave the number as 0.0078.
Step 3: Final Answer
The number 0.00784 rounded to two significant figures is 0.0078.
Summary:
Rounding a number involves identifying the significant figures, counting them appropriately, and then using standard rounding rules to adjust the digits. By focusing on the digits that contribute to the precision of the number, we ensure that the rounded result accurately reflects the desired level of precision.