Place Value and Hundredths Worksheet for identifying decimal numbers using place value grids.

Let’s solve each part step by step.

We are looking at place value grids for decimal numbers up to hundredths. Each grid has three columns: Ones, Tenths, and Hundredths.

- A dot (●) in the Ones column means 1 whole unit.
- Dots or circles in the Tenths column represent tenths — each circle = 0.1
- Circles in the Hundredths column represent hundredths — each circle = 0.01

Note: In some grids, there is a black dot (●) in the Ones column — that means “1” in the ones place. If there’s no dot, it’s 0.

Also note: The problem says “There are ___ tenths and ___ hundredths.” So we count only the circles in those columns — not the black dot in Ones.

Then we write the full decimal number:
→ Ones digit + Tenths digit + Hundredths digit → e.g., 0.23 or 1.45

---

(a)
Grid:
- Ones: one black dot → so 1 one? Wait — look again. Actually, in (a), the black dot is under “Ones”, but then there’s another black dot under “Tenths”? No — let me re-read.

Actually, looking carefully:

In all grids, the black dot (●) appears either in Ones or Tenths — but actually, from the layout, it seems the black dot indicates where the decimal point is? Or maybe it's indicating which column has the "unit"?

Wait — let’s check standard interpretation.

Actually, in these types of worksheets, the black dot usually represents the decimal point position — but here, it’s placed *in* a column.

Looking at grid (a):

Columns: Ones | ● | Tenths | Hundredths
But the ● is between Ones and Tenths? That would be the decimal point.

Wait — no, in the table, the header is:

Ones | ● | Tenths | Hundredths

That suggests the ● is separating Ones and Tenths — meaning it’s the decimal point marker.

But then in row below, there are dots/circles in the cells.

In (a):

Under “Ones”: nothing? Wait — no, in the cell under “Ones”, there is a black dot? Let me parse the image description again.

Actually, based on typical such worksheets:

The black dot (●) shown in the grid is likely indicating the value in that place — but that doesn’t make sense because in (a), under “Ones” there’s a black dot, and under “Tenths” there’s also a black dot? That can’t be.

Wait — perhaps I misread.

Let me reinterpret based on common usage:

In many UK primary worksheets like this (from Teacher-of-Primary.co.uk), the black dot (●) in the grid represents one unit in that place value column.

So:

- If there’s a ● in “Ones”, that’s 1.
- If there’s a ● in “Tenths”, that’s 0.1 — but usually they use circles for fractional parts.

Wait — looking at the grids:

In (a):

- Under “Ones”: one black dot → so 1 one? But then under “Tenths”: one black dot? And under “Hundredths”: three circles?

That would be 1 + 0.1 + 0.03 = 1.13 — but the question says “There are ___ tenths and ___ hundredths.” — implying we ignore the ones? Or include?

Wait — read the instruction: “Which decimal numbers are represented...”

And the fill-in: “There are ___ tenths and ___ hundredths. The decimal number is _____”

This suggests that the “tenths” and “hundredths” refer to the digits after the decimal point — so we need to know what’s in the ones place too.

But in the grid, if there’s a black dot in “Ones”, that’s 1; if in “Tenths”, that might be confusing.

Alternative interpretation (more likely):

The black dot (●) is used to mark the presence of a digit in that place, and circles (○) are counters for how many.

But in (a), under “Ones”: one black dot → so 1 in ones place.

Under “Tenths”: one black dot → so 1 in tenths place? But then why are there circles in hundredths?

This is inconsistent.

Wait — let’s look at grid (b):

Ones: one black dot → 1

Tenths: two circles → 2 tenths

Hundredths: six circles → 6 hundredths

So decimal = 1.26

Similarly, grid (c):

Ones: one black dot → 1

Tenths: five circles → 5 tenths

Hundredths: one circle → 1 hundredth → 1.51

Grid (d):

Ones: one black dot → 1

Tenths: four circles → 4 tenths

Hundredths: nine circles → 9 hundredths → 1.49

Grid (e):

Ones: one black dot → 1

Tenths: zero? No circles → 0 tenths

Hundredths: seven circles → 7 hundredths → 1.07

Grid (f):

Ones: one black dot → 1

Tenths: seven circles → 7 tenths

Hundredths: two circles → 2 hundredths → 1.72

Now back to (a):

Ones: one black dot → 1

Tenths: one black dot? Or is that a circle? In the user’s image description, it says for (a):

“There are ____ tenths and ____ hundredths.”

And in the grid: under Tenths, there is a black dot? Or is it a circle?

Looking back at original text:

For (a):
"Ones • Tenths Hundredths" — the • is probably the separator.

Then in the row:

Under Ones: blank? Or has a dot?

Actually, in the ASCII-like representation given:

(a)
Ones | • | Tenths | Hundredths
| | • | ○ ○
| | | ○

Wait — the user wrote:

"(a)
Ones • Tenths Hundredths
• ○ ○
○"

So under "Ones": nothing? Under "Tenths": a black dot (•)? Under "Hundredths": three circles (○)

But that would mean:

- Ones: 0
- Tenths: 1 (because of the black dot)
- Hundredths: 3

So decimal = 0.13

And the sentence: “There are 1 tenth and 3 hundredths. The decimal number is 0.13”

Similarly, for (b):

"Ones • Tenths Hundredths
• ○ ○ ○ ○ ○
○ ○ ○ ○"

So:

- Ones: black dot → 1
- Tenths: two circles → 2
- Hundredths: six circles → 6
→ 1.26

But wait — in (b), under Tenths, there are two circles, and under Hundredths, six circles — yes.

In (a), under Tenths, there is a black dot — which might mean 1 tenth, and under Hundredths, three circles → 3 hundredths.

But why use black dot for tenths in (a) but circles in others?

Perhaps the black dot in the place value column means “1” for that place, and circles are additional? But that doesn't fit.

Another possibility: the black dot is always in the “Ones” column to indicate the start, but in (a), it's under Tenths? That doesn't make sense.

Let me check online or standard practice.

Since this is a known worksheet type, I recall that in these grids:

- The black dot (●) in the header row is just a separator (like the decimal point).
- Then in the data rows, any symbol in a column represents quantity in that place.
- Typically, a filled circle or dot means 1, and open circles mean 1 each.

But in (a), under "Tenths", there is a black dot — which might be meant to be a counter, same as circles.

Perhaps all symbols (black dot or white circle) represent 1 unit in that place.

In (a):

- Ones: no symbol → 0
- Tenths: one black dot → 1
- Hundredths: three white circles → 3
→ 0.13

In (b):

- Ones: one black dot → 1
- Tenths: two white circles → 2
- Hundredths: six white circles → 6
→ 1.26

In (c):

- Ones: one black dot → 1
- Tenths: five white circles → 5
- Hundredths: one white circle → 1
→ 1.51

In (d):

- Ones: one black dot → 1
- Tenths: four white circles → 4
- Hundredths: nine white circles → 9
→ 1.49

In (e):

- Ones: one black dot → 1
- Tenths: no symbols → 0
- Hundredths: seven white circles → 7
→ 1.07

In (f):

- Ones: one black dot → 1
- Tenths: seven white circles → 7
- Hundredths: two white circles → 2
→ 1.72

This makes sense.

Now for (a): if under Tenths there is a black dot, and it's counted as 1 tenth, and hundredths have 3 circles, then:

"There are 1 tenth and 3 hundredths. The decimal number is 0.13"

Similarly, for others.

But in the grid for (a), is the black dot under "Tenths" meant to be a counter? Yes, likely.

Perhaps the black dot is used interchangeably with circles to represent 1.

So let's go with that.

Thus:

(a)
- Tenths: 1 (black dot)
- Hundredths: 3 (circles)
→ Decimal: 0.13

(b)
- Tenths: 2
- Hundredths: 6
→ Decimal: 1.26 (since ones has 1)

(c)
- Tenths: 5
- Hundredths: 1
→ Decimal: 1.51

(d)
- Tenths: 4
- Hundredths: 9
→ Decimal: 1.49

(e)
- Tenths: 0
- Hundredths: 7
→ Decimal: 1.07

(f)
- Tenths: 7
- Hundredths: 2
→ Decimal: 1.72

Now, verify the counts:

For (a):
Grid shows:
Ones: empty
Tenths: one black dot → 1
Hundredths: three circles → 3
Yes.

For (b):
Ones: one black dot → 1
Tenths: two circles → 2
Hundredths: six circles → 6 (three on top, three on bottom? User said "○ ○ ○" twice, so 6)
Yes.

For (c):
Ones: 1
Tenths: five circles (user said "○ ○ ○" and "○ ○" — wait, in text: "Tenths: ○ ○ ○ \n ○ ○" — that's 5? Three and two is five, yes)
Hundredths: one circle → 1
Yes.

For (d):
Ones: 1
Tenths: four circles ("○ ○ \n ○ ○") → 4
Hundredths: nine circles ("○ ○ ○ \n ○ ○ ○ \n ○ ○ ○") → 9
Yes.

For (e):
Ones: 1
Tenths: no circles → 0
Hundredths: seven circles ("○ ○ \n ○ ○ ○ \n ○ ○") — that's 2+3+2=7? User said: "Hundredths: ○ ○ \n ○ ○ ○ \n ○ ○" — yes, 7
Yes.

For (f):
Ones: 1
Tenths: seven circles ("○ ○ ○ \n ○ ○ ○ \n ○") — 3+3+1=7
Hundredths: two circles ("○ \n ○") — 2
Yes.

Perfect.

So now fill in:

(a) There are 1 tenth and 3 hundredths. The decimal number is 0.13

(b) There are 2 tenths and 6 hundredths. The decimal number is 1.26

(c) There are 5 tenths and 1 hundredth. The decimal number is 1.51

(d) There are 4 tenths and 9 hundredths. The decimal number is 1.49

(e) There are 0 tenths and 7 hundredths. The decimal number is 1.07

(f) There are 7 tenths and 2 hundredths. The decimal number is 1.72

Note: For (c), it says "hundredth" singular, since it's 1.

All good.

Final Answer:

(a) 1, 3, 0.13
(b) 2, 6, 1.26
(c) 5, 1, 1.51
(d) 4, 9, 1.49
(e) 0, 7, 1.07
(f) 7, 2, 1.72