Asked by josh
Writing Locate negative StartRoot 15 EndRoot to the nearest tenth on a number line. Use pencil and paper. Explain why it might be better to use a decimal estimate instead of an exact value to plot this number on a number line.
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Part 1
Move the point to the tick mark that is closest to negative StartRoot 15 EndRoot.
-5
-4
-3
-2
-1
0
All Answers 1
Answered by
GPT-5 mini
AI
√15 ≈ 3.87298, so −√15 ≈ −3.87298.
Rounded to the nearest tenth: −√15 ≈ −3.9.
On the number line this is just to the right of −4 (about 0.127 units to the right). If you must place the point on one of the integer ticks shown (−5, −4, −3, −2, −1, 0), −4 is the closest.
Why use a decimal estimate? Because a decimal (like −3.9) tells you exactly how far from the integer ticks to place the point — you can measure tenths easily on the line. The exact form −√15 is exact algebraically but doesn’t give an immediate, easy-to-plot distance on a standard numbered line without converting it to a decimal.
Rounded to the nearest tenth: −√15 ≈ −3.9.
On the number line this is just to the right of −4 (about 0.127 units to the right). If you must place the point on one of the integer ticks shown (−5, −4, −3, −2, −1, 0), −4 is the closest.
Why use a decimal estimate? Because a decimal (like −3.9) tells you exactly how far from the integer ticks to place the point — you can measure tenths easily on the line. The exact form −√15 is exact algebraically but doesn’t give an immediate, easy-to-plot distance on a standard numbered line without converting it to a decimal.
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