A Peek Beyond the Point: questions with answers

One tenth is 10 hundredths, so 3 tenths are 30 hundredths, and with the 7 hundredths already there that is 37. Adding the two counts instead gives 10, which merges two different places into one.

3 tenths. Written as decimals, 29 hundredths is 0.29, 3 tenths is 0.3 and 9 thousandths is 0.009. The tenths place decides: 0.3 has the most tenths, so 3 tenths is the greatest. Naming a smaller place never makes a part bigger.

The counts differ by 45 tenths. Every ten tenths make one whole unit, so the difference is $4\frac{5}{10}$. The answer 45 treats tenths as whole units.

Each term is $1\frac{1}{10}$ more than the one before. Adding that step takes the tenths to 18. Ten tenths make one whole unit, so the term is $9\frac{8}{10}$. Leaving the tenths at 18 gives $8\frac{18}{10}$.

12.6 has no hundredths of its own, so one tenth is borrowed and arrives as ten of them: 3.51. Bringing the 9 hundredths straight down instead of subtracting it gives 3.69 -- which is more than 3.51, though something has just been taken away.

The columns were lined up from the right instead of by place. 0.6 was pushed right until its last digit sat under the last digit of 0.934, so its 6 was counted as 6 thousandths instead of 6 tenths. The right answer is 1.534, and nothing here is a carrying mistake: the columns themselves were wrong.

0.20. A zero written at the end says there are no hundredths, which was already true, so nothing changes. In 0.02 the zero pushes the 2 into a smaller place, making it a tenth of what it was. 2 is a whole number, but in 0.2 the 2 counts tenths.

They are equal: 13.800 is 13.8 with two zeros written on the end, and a zero at the end adds no parts. The longer form has more digits but not more quantity -- every place they both have holds the same digit.

The number below the line says which place the digits end in: tenths end one place after the point, so $\frac{12}{10}$ is 1.2. 12 is what the next place up would give, and 0.12 what the next place down would give.

Each whole unit is 10 tenths, so 23 units are 230 tenths, and with the 4 already after the point that is 234. The tenths are not only what stands after the point -- that would be 4 -- and 2340 is the count of HUNDREDTHS.

The ten divisions share one tenth, so one division is 0.01, and the mark stands four divisions along: 1.04. Calling every division a tenth gives 1.4, and counting the divisions as whole units gives 5.

The line spans one hundredth, and ten divisions share it, so each one is 0.001. A division is only a tenth when the line spans exactly one unit; here 0.1 would make the line span 1 unit instead.

Each charge is 20 paise, which is ₹0.20, and there are 15,000 of them: ₹3,000. Reading the paise as tenths of a rupee makes each charge ₹2 and the total ₹30,000, ten times too much, while ₹3,00,000 leaves the paise counted as whole rupees.

1000 mm make 1 m, so 8 mm is 8 thousandths of a meter. Thousandths sit in the third place after the point, so the tenths place and the hundredths place are empty and each holds a zero. That gives 3.008 m. Putting the smaller unit's count straight after the point gives 3.8 m, which is a far bigger quantity.

7.5. They are not the same quantity: the zero in 7.05 holds the tenths place, so its 5 is worth 5 hundredths where the other number's is worth 5 tenths -- ten times more.