Question

1. what is the result of the following calculation? record to the correct number of significant figures. 7.520 ml + 0.01509 ml = ? 7.535 ml 7.53509 ml 7.53 ml 7.5351 ml

Explanation:

Step1: Perform the addition

First, add the two volumes: \(7.520\space mL + 0.01509\space mL = 7.53509\space mL\)

Step2: Determine significant figures for addition

When adding, the result should have the same number of decimal places as the least precise measurement. \(7.520\) has three decimal places, \(0.01509\) has five decimal places. So we round to three decimal places. Rounding \(7.53509\) to three decimal places gives \(7.535\space mL\)? Wait, no, wait. Wait, \(7.520\) has three decimal places (the zero at the end is significant, so decimal places: 7.520 is to the thousandth place, 0.01509 is to the hundred - thousandth place). Wait, no, the rule for addition/subtraction is that the result has the same number of decimal places as the number with the least number of decimal places. \(7.520\) has 3 decimal places (the digits after the decimal: 5,2,0), \(0.01509\) has 5 decimal places. So we go with 3 decimal places. Let's re - calculate the sum: \(7.520+0.01509 = 7.53509\). Now, rounding to three decimal places: look at the fourth decimal place, which is 0. Wait, no, 7.520 is 7.520 (three decimal places: tenths, hundredths, thousandths: 5,2,0), 0.01509 is 0.01509 (five decimal places: tenths:0, hundredths:1, thousandths:5, ten - thousandths:0, hundred - thousandths:9). When adding, \(7.520 + 0.01509=7.53509\). Now, the number of decimal places: 7.520 has 3 decimal places, so the sum should be rounded to 3 decimal places. 7.53509 rounded to 3 decimal places: the third decimal place is 5, the next digit is 0, so it remains 7.535? Wait, no, wait 7.520 is 7.520 (milliliters), so the precision is to the thousandth of a milliliter. 0.01509 is to the hundred - thousandth. So when adding, we add them as is, then round to the thousandth place. \(7.520+0.01509 = 7.53509\). Rounding to three decimal places: the digit in the fourth decimal place is 0, which is less than 5, so we keep the third decimal place as is. Wait, but 7.53509 to three decimal places is 7.535? But wait, let's check the significant figures again. Wait, 7.520 has four significant figures, 0.01509 has four significant figures (the leading zeros don't count, so 1,5,0,9). When adding, the decimal places matter. 7.520 is 7.520 (three decimal places), 0.01509 is 0.01509 (five decimal places). So the sum should be reported to three decimal places. So \(7.53509\) rounded to three decimal places is \(7.535\space mL\)? But wait, let's check the options. Wait, maybe I made a mistake. Wait, 7.520 is 7.520 (the zero at the end is significant, so it's 7.520, which is to the thousandth place). 0.01509 is 0.01509, to the hundred - thousandth. So adding them: 7.520 + 0.01509 = 7.53509. Now, for addition, the number of decimal places in the result is equal to the number of decimal places in the term with the least number of decimal places. 7.520 has 3 decimal places, so the result should have 3 decimal places. So 7.53509 rounded to 3 decimal places is 7.535 (since the fourth decimal is 0, which is less than 5, so we don't round up the third decimal). Wait, but let's check the options. One of the options is 7.535 mL. Wait, but let's re - evaluate. Wait, 7.520 is 7.520 (milliliters), so the precision is ±0.001 mL, and 0.01509 is ±0.00001 mL. When adding, the absolute error is the sum of the absolute errors, but for significant figures in addition, it's about decimal places. So 7.520 (3 decimal places) + 0.01509 (5 decimal places) = 7.53509, which should be rounded to 3 decimal places: 7.535 mL. Wait, but let's check the calculation again: 7.520+0.01509: 7.520 is 7.52000 (if we write it to five decimal places), then 7.52000+0.01509 = 7.53509. Now, rounding to three decimal places: the third decimal is 5, the fourth is 0, so it's 7.535. So the correct answer should be 7.535 mL.

Answer:

7.535 mL