Chapter 3, Problem 3.1P

(a)

Interpretation Introduction

Interpretation:

The given number has to be rounded to four significant figures.

Concept Introduction:

Significant Figures:

While reporting a reading of a measurement, the digits that are considered to be significant irrespective of the place of location of decimal point are called significant figures.

All the digits in a measurement except zero are considered significant, whereas zero is considered as significant only when it lies in the middle of the digit or at the end of number on the right-hand side of a decimal point.

Rounding off:

Rounding off a simpler numeral by maintaining the value close to its original value.

Steps for Rounding off:

• The location of rounding should be found.
• If the next digit after the rounding place is greater than 5 (i.e 5, 6, 7, 8 or 9) the value will be rounded up.
• If the next digit after the rounding place is lesser than 5, (i.e 0, 1, 2, 3 or 4) the value will be rounded down.

Answer to Problem 3.1P

The given number is rounded to four significant figures as $1.237$

Explanation of Solution

Given data:

The given number is $1.2367$

Rounding off:

The next digit after the rounding place is seven which is greater than five. Hence, the given value is rounded up at the fourth place.

Therefore, the given number is rounded as $\left(1.237\right).$

Conclusion

The given number is rounded to four significant figure as $1.237$.

(b)

Interpretation Introduction

Interpretation:

The given number has to be rounded to four significant figures.

Concept Introduction:

Refer part (a).

Answer to Problem 3.1P

The given number is rounded to four significant figure as $\left(1.238\right).$

Explanation of Solution

Given data:

The given number is $1.2384$

Rounding off:

The next digit after the rounding place is four which is lesser than five. Hence, the given value is rounded down at the fourth place.

Therefore, the given number is rounded as $1.238.$

Conclusion

The given number is rounded to four significant figure as $1.238.$

(c)

Interpretation Introduction

Interpretation:

The given number has to be rounded to three significant figures.

Concept Introduction:

Refer part (a).

Answer to Problem 3.1P

The given number is rounded to three significant figure as $0.135.$

Explanation of Solution

Given data:

The given number is $0.1352.$

Rounding off:

The next digit after the round place is two which is lesser than five. Hence, the given value is rounded down at the third place.

Therefore, the given number is rounded as $0.135.$

Conclusion

The given number is rounded to three significant figures as $0.135.$

(d)

Interpretation Introduction

Interpretation:

The given number has to be rounded to two significant figures.

Concept Introduction:

Refer part (a).

Answer to Problem 3.1P

The given number is rounded to two significant figure as $2.1.$

Explanation of Solution

Given data:

The given number is $2.051.$

Rounding off:

The next digit after the round place is five which is equal to five. Hence, the given value is rounded up at the second place.

Therefore, the given number is rounded as $2.1.$

Conclusion

The given number is rounded to two significant figure as $2.1.$

(e)

Interpretation Introduction

Interpretation:

The given number has to be rounded to three significant figures.

Concept Introduction:

Refer part (a).

Answer to Problem 3.1P

The given number is rounded to three significant figure as $2.01.$

Explanation of Solution

Given data:

The given number is $2.0050.$

Rounding off:

The next digit after the round place is five which is equal to five. Hence, the given value is rounded up at the third place.

Therefore, the given number is rounded as $2.01.$

Conclusion

The given number is rounded to three significant figures as $2.01.$