Write the number which has:I. $$2$$ tens, $$3$$ ones, $$1$$ tenths and $$3$$ hundredths.II. $$1$$ hundreds, $$2$$ ones, $$2$$ hundredths and $$3$$ tenths.III. $$2$$ hundreds, 3tens, $$5$$ ones, $$3$$ hundredths, $$2$$ tenths and $$1$$ thousandths.IV. $$3$$ hundreds, $$1$$ tens, $$5$$ ones, $$2$$ tenths, $$1$$ hundredths and $$4$$ thousandths.

Question

Write the number which has:I. $$2$$ tens,  $$3$$ ones,  $$1$$ tenths and  $$3$$ hundredths.II. $$1$$ hundreds,  $$2$$ ones,  $$2$$ hundredths and  $$3$$ tenths.III. $$2$$ hundreds, 3tens,  $$5$$ ones,  $$3$$  hundredths,  $$2$$ tenths and  $$1$$  thousandths.IV. $$3$$ hundreds,  $$1$$  tens,  $$5$$ ones,  $$2$$ tenths,  $$1$$ hundredths and  $$4$$  thousandths.

Vedantu Content Team · Accepted Answer

Hint: In Hindu-Arabic system, we have ten digits, namely  $$0,1,2,3,4,5,6,7,8$$ and  $$9$$ .A number is denoted by a group of digits, called numeral.For denoting a numeral, we use the place-value chart.For any counting number  $$n$$ following holds  $$n$$ ones $$ = n \times 1$$  $$n$$ tens $$ = n \times 10$$  $$n$$ hundreds $$ = n \times 100$$  $$n$$ thousands $$ = n \times 1000$$  $$n$$ tenths $$ = n \times \dfrac{1}{{10}}$$  $$n$$ hundredths $$ = n \times \dfrac{1}{{100}}$$  $$n$$ thousandths $$ = n \times \dfrac{1}{{1000}}$$ .Using the above formulas, we find the number.Complete step-by-step answer:(a)Given  $$2$$  tens,  $$3$$ ones,  $$1$$ tenths and  $$3$$ hundredths.Then the number is  $$2$$ tens $$ + $$  $$3$$ ones $$ + $$  $$1$$ tenths $$ + $$  $$3$$ hundredthsSince  $$2$$  tens $$ = 2 \times 10 = 20$$ ,  $$3$$ ones $$ = 3 \times 1 = 3$$ ,  $$1$$ tenths $$ = 1 \times \dfrac{1}{{10}} = 0.1$$  and  $$3$$ hundredths $$ = 3 \times \dfrac{1}{{100}} = 0.03$$ .Then the number is  $$20 + 3 + 0.1 + 0.03 = 23.13$$ .(b)Given  $$1$$ hundreds,  $$2$$ ones,  $$2$$ hundredths and  $$3$$ tenths.Then the number is  $$1$$ hundreds $$ + $$  $$2$$ ones $$ + $$  $$2$$ hundredths  $$ + $$  $$3$$ tenths.Since  $$1$$ hundreds $$ = 1 \times 100 = 100$$ ,  $$2$$ ones $$ = 2 \times 1 = 2$$ ,  $$2$$ hundredths $$ = 2 \times \dfrac{1}{{100}} = 0.02$$  and  $$3$$ tenths $$ = 3 \times \dfrac{1}{{10}} = 0.3$$ .Then the number is  $$100 + 2 + 0.02 + 0.3 = 102.32$$ .(c)Given  $$2$$ hundreds, 3tens,  $$5$$ ones,  $$3$$  hundredths,  $$2$$ tenths and  $$1$$  thousandths.Then the number is  $$2$$ hundreds $$ + $$ 3 tens $$ + $$   $$5$$ ones $$ + $$  $$3$$  hundredths $$ + $$  $$2$$ tenths  $$ + $$  $$1$$ thousandths.Since  $$2$$ hundreds $$ = 2 \times 100 = 200$$ , 3 tens $$ = 3 \times 10 = 30$$ ,  $$5$$ ones $$ = 5 \times 1 = 5$$ ,  $$3$$ hundredths $$ = 3 \times \dfrac{1}{{100}} = 0.03$$ ,  $$2$$ tenths  $$ = 2 \times \dfrac{1}{{10}} = 0.2$$  and  $$1$$  thousandths $$ = 1 \times \dfrac{1}{{1000}} = 0.001$$ .Then the number is $$200 + 30 + 5 + 0.03 + 0.2 + 0.001 = 235.231$$ . (d)Given  $$3$$ hundreds,  $$1$$  tens,  $$5$$ ones,  $$2$$ tenths,  $$1$$ hundredths and  $$4$$  thousandths.Then the number is  $$3$$ hundreds $$ + $$  $$1$$  tens $$ + $$  $$5$$ ones $$ + $$  $$2$$ tenths $$ + $$  $$1$$ hundredths $$ + $$  $$4$$ thousandths.Since  $$3$$ hundreds $$ = 3 \times 100 = 300$$ ,  $$1$$  tens $$ = 1 \times 10 = 10$$ ,  $$5$$ ones $$ = 5 \times 1 = 5$$ ,  $$2$$ tenths $$ = 2 \times \dfrac{1}{{10}} = 0.2$$ ,  $$1$$ hundredths $$ = 1 \times \dfrac{1}{{100}} = 0.01$$  and  $$4$$ thousandths $$ = 4 \times \dfrac{1}{{1000}} = 0.004$$ .Then the number is $$300 + 10 + 5 + 0.2 + 0.01 + 0.004 = 315.214$$ .Note: Note that the place value of  $$0$$  in a given number is  $$0$$ , at whatever place it may be. The face value of a digit in a numeral is its own value, at whatever place it may be. In the numeral  $$8709$$ , the face value of  $$7$$ is  $$7$$ and the face value of  $$8$$ is  $$8$$ but the place value of  $$8$$ is  $$8000$$ .